Examination of the Effects of Curvature in Geometrical Space on Accuracy of Scaling Derived Projections of Plant Biomass Units: Applications to the Assessment of Average Leaf Biomass in Eelgrass Shoots

Table 1

Summary of notation convention of the bivariate scaling model of (1) and its generalization to account for curvature as given by (3). GS stands for geometrical space, AS stands for arithmetical space, and CF means correction factor of retransformation bias.

	Typical bivariate	Eq.	Generalized for curvature	Eq.
Basic form		(1)		(3)
Regression equation in GS		(2), (D.1)		(4)
Mean response GS		(B.4)		(B.1)
Back transformation AS		(B.5)		(B.2)
Mean response AS		(B.6)		(B.3)
CF Baskerville		(B.6), (C.1)		(B.3), (C.1)
CF Duan		(B.6), (C.2)		(B.3), (C.2)
CF Zeng and Tang		(B.6), (C.3)		(B.3), (C.3)
CF n-partial sum		(B.6), (C.4)		(B.3), (C.4)